Question: Simplify the following expression: $y = \dfrac{9k^2 + 126k + 405}{k + 5} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $9$ , so we can rewrite the expression: $ y =\dfrac{9(k^2 + 14k + 45)}{k + 5} $ Then we factor the remaining polynomial: $k^2 + {14}k + {45} $ ${5} + {9} = {14}$ ${5} \times {9} = {45}$ $ (k + {5}) (k + {9}) $ This gives us a factored expression: $\dfrac{9(k + {5}) (k + {9})}{k + 5}$ We can divide the numerator and denominator by $(k - 5)$ on condition that $k \neq -5$ Therefore $y = 9(k + 9); k \neq -5$